Question

if(x+1/x)^2=3 then value of x^54+x^48+x^42+x^36

Answer 1

Answer:

4

Step-by-step explanation:

(x+1/x)^2=3

now x^2+1+2x/x^2=3

x^2+2x+1=3x^2

3x^2-x^2-2x-1=0

2x^2-2x-1=0

now factorise

2x^2-2x+x-1=0

2x(x-1)+1(x-1)=0

(x-1)(2x+1)=0

x=1,-1/2

now put x=1

x^54+x^48+x^42+x^36

=1+1+1+1

=4